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A vector v is equally inclined to the X-axis, Y-axis and Z-axis respectively the dirction cosines areA. `lt (1)/(sqrt3),(1)/(sqrt3),(1)/(sqrt3)gt`B. `lt -(1)/(sqrt3), -(1)/(sqrt3), -(1)/(sqrt3)gt`C. `lt (1)/(sqrt3), (1)/(sqrt3), (1)/(sqrt3)gt or lt -(1)/(sqrt3), -(1)/(sqrt3), -(1)/(sqrt3)gt`D. None of the above |
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Answer» Correct Answer - C Let the vecto v make an angle `alpha` with each of the three axes, then diractin consine of v are `lt cos alpha, cos alpha, cos alphagt` Also, `cos ^(2)alpha +cos ^(2)alpha+cos ^(2)alpha=1` `impliescos ^(2)alpha =1//3` `impliescos alpha =pm(1)/(sqrt3)` Hence, direction cosine of v are `lt (1)/(sqrt3),(1)/(sqrt3), (1)/(sqrt3)gt` or `lt-(1)/(sqrt3), -(1)/(sqrt3),-(1)/(sqrt3)gt` |
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